Properties

Label 576.3.b
Level $576$
Weight $3$
Character orbit 576.b
Rep. character $\chi_{576}(415,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $5$
Sturm bound $288$
Trace bound $25$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 576.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(288\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(576, [\chi])\).

Total New Old
Modular forms 216 20 196
Cusp forms 168 20 148
Eisenstein series 48 0 48

Trace form

\( 20 q + O(q^{10}) \) \( 20 q - 24 q^{17} - 172 q^{25} - 24 q^{41} - 108 q^{49} + 192 q^{65} - 88 q^{73} + 168 q^{89} - 536 q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(576, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
576.3.b.a $4$ $15.695$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{5}+5\zeta_{12}q^{7}-2\zeta_{12}^{3}q^{11}+\cdots\)
576.3.b.b $4$ $15.695$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-6}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{5}-5\beta _{1}q^{7}+\beta _{3}q^{11}-71q^{25}+\cdots\)
576.3.b.c $4$ $15.695$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{7}+\zeta_{12}^{2}q^{13}-\zeta_{12}^{3}q^{19}+\cdots\)
576.3.b.d $4$ $15.695$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{5}+\zeta_{12}^{3}q^{7}-\zeta_{12}q^{11}+\cdots\)
576.3.b.e $4$ $15.695$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{5}-\zeta_{12}q^{7}+2\zeta_{12}^{3}q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(576, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(576, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)